Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 4, Problem 4.52P
Consider the square channel shown in the sketch operating under steady-state conditions. The inner surface of the channel is at a uniform temperature of 600K, while the outer surface is exposed to convection with a fluid at 300 K and a convection coefficient of
- Beginning with properly defined control volumes, derive the finite-difference equations for nodes 2, 4, and 7 and determine the temperatures
- Calculate the heat loss per unit length from the channel.
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Consider the square channel shown in the sketch operating under steady state condition. The inner surface of the
channel is at a uniform temperature of 600 K and the outer surface is at a uniform temperature of 300 K. From a
symmetrical elemental of the channel, a two-dimensional grid has been constructed as in the right figure
below. The points are spaced by equal distance.
Tout = 300 K
k = 1 W/m-K
T = 600 K
(a) The heat transfer from inside to outside is only by conduction across the channel wall. Beginning with
properly defined control volumes, derive the finite difference equations for locations 123. You can
also use (n, m) to represent row and column. For example, location Dis (3, 3), location is (3,1), and
location 3 is (3,5). (hint: I have already put a control volume around this locations with dashed boarder.)
(b) Please use excel to construct the tables of temperatures and finite difference. Solve for the temperatures
of each locations. Print out the tables in the spread…
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1/2
Sn = Sn. [a + b(r)]
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To
A solid cylinder of radius R and length L is made from material with thermal conductivity 2.
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Chapter 4 Solutions
Fundamentals of Heat and Mass Transfer
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